As long as MS dont find you using a modchip you are fine to update your live dashboard. and can even play and download stuff... if they find you using a mod chi console then they will ban oyr console set and not your ID. so you can buy/re-mod your console to go back online with sam ID.
actual HD quality is 1080P. as long as you are getting a 1080P output you are fine to go with any cable... in above picture VGA picture has got 1080P , so its much better.
MS has now commenced a new kind of banning its different than modchip ban. you should all check this one out.
MS Take Action Against LIVE Cheaters